Emily is 2 times as old as Umaima. Six years ago, Emily was 5 times as old as Umaima. How old is Emily now?
Answer: We can use the given information to write down two equations that describe the ages of Emily and Umaima. Let Emily's current age be $e$ and Umaima's current age be $u$ The information in the first sentence can be expressed in the following equation: $e = 2u$ Six years ago, Emily was $e - 6$ years old, and Umaima was $u - 6$ years old. The information in the second sentence can be expressed in the following equation: $e - 6 = 5(u - 6)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $e$ , it might be easiest to solve our first equation for $u$ and substitute it into our second equation. Solving our first equation for $u$ , we get: $u = e / 2$ . Substituting this into our second equation, we get: $e - 6 = 5($ $(e / 2)$ $- 6)$ which combines the information about $e$ from both of our original equations. Simplifying the right side of this equation, we get: $e - 6 = \dfrac{5}{2} e - 30$ Solving for $e$ , we get: $\dfrac{3}{2} e = 24$ $e = \dfrac{2}{3} \cdot 24 = 16$.